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Quantitative relative entropy estimates for interacting particle systems with common noise

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arxiv 2407.01217 v1 pith:E7XJKUA6 submitted 2024-07-01 math.PR math.AP

Paul Nikolaev This is my paper · ORCID
classification math.PRmath.AP
keywords commonconditionalentropyequationestimatesidiosyncraticinteractinglarge
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abstract

We derive quantitative estimates proving the conditional propagation of chaos for large stochastic systems of interacting particles subject to both idiosyncratic and common noise. We obtain explicit bounds on the relative entropy between the conditional Liouville equation and the stochastic Fokker--Planck equation with an interaction kernel \(k\in L^2(\R^d) \cap L^\infty(\R^d)\), extending far beyond the Lipschitz case. Our method relies on reducing the problem to the idiosyncratic setting, which allows us to utilize the exponential law of large numbers by Jabin and Wang~\cite{JabinWang2018} in a pathwise manner.

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Cited by 3 Pith papers

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  1. A Shared Observation Shields Collective Fluctuations while Preserving Local Independence

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    Conditioning an exchangeable population on its own noisy collective record produces a rank-one, nonpositive Schur shield correction to collective fluctuations while keeping pair correlations at O(1/z), giving a calcul...

  2. The fluctuation behaviour of the stochastic point vortex model with common noise

    math.PR 2025-01 conditional novelty 6.0 of 10

    The fluctuation process of the stochastic point vortex model with common noise converges in distribution to the unique strong solution of a linear fluctuation SPDE with multiplicative transport noise and a conditional...

  3. Quantitative particle approximation of nonlinear stochastic Fokker-Planck equations with singular kernel

    math.PR 2024-12 conditional novelty 6.0 of 10

    The paper derives explicit N^{-κ} error bounds for the mollified empirical measure of moderately interacting particles with common noise, and proves local strong well-posedness of the limiting stochastic Fokker-Planck...

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